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On global and local minimizers of prestrained thin elastic rods

Abstract

We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By \(\Gamma \)-convergence we derive a one-dimensional limit theory and show that isolated local minimizers of the limit model can be approached by local minimizers of the three-dimensional model. In the case of isotropic materials and for two-layers prestrained three-dimensional models the limit energy further simplifies to that of a Kirchhoff rod-model of an intrinsically curved beam. In this case we study the limit theory and investigate global and/or local stability of straight and helical configurations.

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Notes

  1. 1.

    We convene that \(x_{*}=2\pi \) if \(\frac{(c_{13}kL)^2}{4\pi ^2c_{12}c_{23}}=1\).

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Correspondence to Marco Cicalese.

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Communicated by J. Ball.

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Cicalese, M., Ruf, M. & Solombrino, F. On global and local minimizers of prestrained thin elastic rods. Calc. Var. 56, 115 (2017). https://doi.org/10.1007/s00526-017-1197-6

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Mathematics Subject Classification

  • 74K10
  • 49J45
  • 49S05